Michael Atiyah gives a presidential address on Mind, Matter, and Mathematics (good alliteration). In it he discusses the difference between mathematical philosophy and natural philosophy. It’s an interesting read throughout.

But, near the end he says:

Mathematical physicists believe that there are indeed simple and beautiful mathematical equations that govern the universe, and that the task of the scientist is to search for them. This is an article of faith.

An alternative faith is to believe in a God who created the universe and kindly provided us with laws or equations that we would be able to understand.

He touts that these are compatible philosophies. As faiths, they are similar (I take issue with the first idea: Mathematical equations do not “govern” the universe, they are just really good at representing it.)

But, more importantly, I disagree with the idea that belief in God is always compatible with science (an implication I think he was making). In physics, it’s an easier sell. There is nothing alive in physics.

A harder sell is in biology. Belief in God is one thing, but belief in a soul is problematic. If one believes in a soul, that every human (homo sapien) is singled out from among God’s creatures as different (better), then all of biological evolution (and what it can tell us about who we are) falls apart.

If it is true that humans ARE totally and fundamentally different than all of the other creatures on earth (and potentially on other planets), and if this is due to our having a soul, then we MUST abandon much of what we believe to be true in biology.

If biology is right, then we are not different in any fundamental way than other species. Unique, sure. (So is the norwhal.) But, not totally different.

I am hesitant to say that a belief in a God-given soul is compatible with biological science, and from there science generally.

It describes how the change in trait with phenotypes is related to the phenotypes’ fitnesses, . Note that the genetics of the trait (mutation, ploidy, etc.) is contained in the second term. See Wikipedia for more details.

Now, of course, that doesn’t mean that we’re all going to hell. But, the movie which was inspired by a book on Darwin may make it seem that way:

“It featured a mathematical equation—W Delta Z—formulated by American population geneticist George R. Price,” he explains. “It supposedly shows that there’s no real altruism in nature; no such thing as selflessness. Price was so upset by his findings that he ended up giving away all his possessions to the poor and, eventually homeless himself, committed suicide with a pair of nail scissors in a filthy London squat.”

Jeffrey Shallit pointed me to a youtube video, in which David Berlinski makes the following remarkable claim: “… von Neumann, one of the great mathematicians of the 20th century, just laughed at Darwinian theory. He hooted at it.”

Thankfully, Douglas L. Theobald goes to some length to clear Von Neumann’s good name, and shows how such nonsense turns out to be … well, nonsense. Von Neumann, one of the greats of Game Theory (and plenty of other maths) clearly believed in evolution and did substantial work in areas of mathematics that have directly affected the field of biological evolution in remarkably positive ways.

Anybody who looks at living organisms knows perfectly well that they can produce other organisms like themselves. This is their normal function, they wouldn’t exist if they didn’t do this, and it’s plausible that this is the reason why they abound in the world. In other words, living organisms are very complicated aggregations of elementary parts, and by any reasonable theory of probability or thermodynamics highly improbable. That they should occur in the world at all is a miracle of the first magnitude; the only thing which removes, or mitigates, this miracle is that they reproduce themselves. Therefore, if by any peculiar accident there should ever be one of them, from there on the rules of probability do not apply, and there will be many of them, at least if the milieu is reasonable. But a reasonable milieu is already a thermodynamically much less improbable thing. So, the operations of probability somehow leave a loophole at this point, and it is by the process of self-reproduction that they are pierced.

Furthermore, it’s equally evident that what goes on is actually one degree better than self-reproduction, for organisms appear to have gotten more elaborate in the course of time. Today’s organisms are phylogenetically descended from others which were vastly simpler than they are, so much simpler, in fact, that it’s inconceivable how any kind of description of the later, complex organisms could have existed in the earlier one. It’s not easy to imagine in what sense a gene, which is probably a low order affair, can contain a description of the human being which will come from it. But in this case you can say that since the gene has its effect only within another human organism, it probably need not contain a complete description of what is to happen, but only a few cues for a few alternatives. However, this is not so in phylogenetic evolution. That starts from simple entities, surrounded by an unliving amorphous milieu, and produces something more complicated. Evidently, these organisms have the ability to produce something more complicated than themselves.

Martin Nowak is certainly not alone when he argues, in Evolutionary Dynamics, that evolution is the single most significant idea in biology. But almost all major mathematical syntheses of evolution have been confined to population genetics–the study of gene frequency changes in populations. By contrast, Nowak (a professor of biology and mathematics at Harvard) follows up on Hardy’s last qualification for a great idea by showing the many ways in which the mathematics of evolution lead to advances in diverse subjects, including cancer, game theory, and language.

New study shows that even college students can perform as well as monkeys on an arithmetic test.

The results indicate that monkeys perform approximate mental addition in a manner that is remarkably similar to the performance of the college students. These findings support the argument that humans and nonhuman primates share a cognitive system for nonverbal arithmetic, which likely reflects an evolutionary link in their cognitive abilities.